EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 9th April 2016>Q 90

MEDIUM

JEE Main

IMPORTANT

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If the tangent at a point $P$ , with parameter $t$ , on the curve $x = 4 t^{2} + 3, y = 8 t^{3} - 1, t \in R,$ meets the curve again at a point $Q$ , then the coordinates of $Q$ are :

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Important Questions on Application of Derivatives

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3rd April 2016>Q 91

Consider

f (x) = \tan^{- 1} (\sqrt{\frac{1 + \sin x}{1 - \sin x}}), x \in (0, \frac{π}{2}) .

A normal to

y = f (x)

at

x = \frac{π}{6}

also passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 3rd April 2016>Q 92

A wire of length

2

units is cut into two parts which are bent respectively to form a square of side

= x

units and a circle of radius

= r

units. If the sum of the areas of the square and the circle so formed is minimum, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2016>Q 93

Let C be a curve given by

y (x) = 1 + \sqrt{4 x - 3}

,

x > \frac{3}{4}

. If

P

is a point on C, such that the tangent at

P

has slope

\frac{2}{3}

, then a point through which the normal at

P

passes, is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2016>Q 94

Let

f (x) = \sin^{4} x + \cos^{4} x .

Then,

f

is an increasing function in the interval:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 10th April 2015>Q 95

The distance from the origin, of the normal to the curve,

x = 2 \cos t + 2 t \sin t, y = 2 \sin t - 2 t \cos t a t t = \frac{π}{4},

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 96

From the top of a

64

metres high tower, a stone is thrown upwards vertically with the velocity of

48 m / s .

The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration

g = 32 m / s^{2}

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 97

The equation of a normal to the curve,

\sin y = x \sin (\frac{π}{3} + y) at x = 0,

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 27 - Application of Derivatives>JEE Main - 11th April 2015>Q 98

Let

k

and

K

be the minimum and the maximum values of the function

f (x) = \frac{{(1 + x)}^{0.6}}{1 + x^{0.6}} in [0, 1]

, respectively, then the ordered pair

(k, K)

is equal to: